### Abstract

The application of importance sampling as a variance reduction technique in Monte Carlo quasiclassical trajectory calculations is discussed. Two measures are proposed which quantify the quality of the importance sampling used, and indicate whether further improvements may be obtained by some other choice of importance sampling function. A general procedure for constructing standardized histogrammic representations of differential functions which integrate to the appropriate integral value obtained from a trajectory calculation is presented. Two criteria for "optimum" binning of these histogrammic representations of differential functions are suggested. These are (1) that each bin makes an equal contribution to the integral value, and (2) each bin has the same relative error. Numerical examples illustrating these sampling and binning concepts are provided.

Original language | English |
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Pages (from-to) | 4087-4096 |

Number of pages | 10 |

Journal | Journal of Chemical Physics |

Volume | 69 |

Issue number | 9 |

Publication status | Published - 1978 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*69*(9), 4087-4096.

**Importance sampling and histogrammic representations of reactivity functions and product distributions in Monte Carlo quasiclassical trajectory calculations.** / Faist, M. B.; Muckerman, James; Schubert, F. E.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 69, no. 9, pp. 4087-4096.

}

TY - JOUR

T1 - Importance sampling and histogrammic representations of reactivity functions and product distributions in Monte Carlo quasiclassical trajectory calculations

AU - Faist, M. B.

AU - Muckerman, James

AU - Schubert, F. E.

PY - 1978

Y1 - 1978

N2 - The application of importance sampling as a variance reduction technique in Monte Carlo quasiclassical trajectory calculations is discussed. Two measures are proposed which quantify the quality of the importance sampling used, and indicate whether further improvements may be obtained by some other choice of importance sampling function. A general procedure for constructing standardized histogrammic representations of differential functions which integrate to the appropriate integral value obtained from a trajectory calculation is presented. Two criteria for "optimum" binning of these histogrammic representations of differential functions are suggested. These are (1) that each bin makes an equal contribution to the integral value, and (2) each bin has the same relative error. Numerical examples illustrating these sampling and binning concepts are provided.

AB - The application of importance sampling as a variance reduction technique in Monte Carlo quasiclassical trajectory calculations is discussed. Two measures are proposed which quantify the quality of the importance sampling used, and indicate whether further improvements may be obtained by some other choice of importance sampling function. A general procedure for constructing standardized histogrammic representations of differential functions which integrate to the appropriate integral value obtained from a trajectory calculation is presented. Two criteria for "optimum" binning of these histogrammic representations of differential functions are suggested. These are (1) that each bin makes an equal contribution to the integral value, and (2) each bin has the same relative error. Numerical examples illustrating these sampling and binning concepts are provided.

UR - http://www.scopus.com/inward/record.url?scp=0001531714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001531714&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001531714

VL - 69

SP - 4087

EP - 4096

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 9

ER -